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Math Problems
Algebra 2
Domain and range of quadratic functions: equations
Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation of the graph
\newline
y
=
−
3
(
2
)
x
y = -3(2)^x
y
=
−
3
(
2
)
x
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Compare the domain and range for
f
(
x
)
=
∣
x
∣
f(x)=|x|
f
(
x
)
=
∣
x
∣
and
g
(
x
)
=
∣
x
∣
g(x)=|x|
g
(
x
)
=
∣
x
∣
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Find the area enclosed by the graphs of
f
(
x
)
=
2
−
x
f(x)=2-x
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
g(x)=x^{2}
g
(
x
)
=
x
2
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Find the area enclosed by the graphs of
f
(
x
)
=
2
−
x
f(x)=2-x
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
g(x)=x^{2}
g
(
x
)
=
x
2
.
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Which equations define
y
y
y
as a nonlinear function of
x
x
x
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
y
=
4
x
4
+
5
y = 4x^4 + 5
y
=
4
x
4
+
5
\newline
(B)
y
=
x
4
y = \frac{x}{4}
y
=
4
x
\newline
(C)
y
=
x
+
2
2
y = x + 2^2
y
=
x
+
2
2
\newline
(D)
4
y
=
3
x
4y = 3x
4
y
=
3
x
\newline
(E)
y
=
5
x
2
y = 5x^2
y
=
5
x
2
\newline
(F)
y
=
3
−
5
x
y = 3 - 5x
y
=
3
−
5
x
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Which equations define
y
y
y
as a nonlinear function of
x
x
x
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
y
=
3
x
2
y = \frac{3x}{2}
y
=
2
3
x
\newline
(B)
y
−
4
=
3
x
2
y - 4 = 3x^2
y
−
4
=
3
x
2
\newline
(C)
y
=
x
5
+
6
y = x^5 + 6
y
=
x
5
+
6
\newline
(D)
2
y
=
12
2y = 12
2
y
=
12
\newline
(E)
y
=
7
x
−
x
y = 7x - x
y
=
7
x
−
x
\newline
(F)
y
=
7
x
×
x
y = 7x \times x
y
=
7
x
×
x
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The set
S
=
{
x
∣
−
2
<
x
<
8
}
S=\{x \mid-2<x<8\}
S
=
{
x
∣
−
2
<
x
<
8
}
is described by which interval notation?
\newline
(
−
2
,
8
)
(-2,8)
(
−
2
,
8
)
\newline
[
−
2
,
8
]
[-2,8]
[
−
2
,
8
]
\newline
[
−
2
,
8
)
[-2,8)
[
−
2
,
8
)
\newline
(
−
2
,
8
]
(-2,8]
(
−
2
,
8
]
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What is the range of this quadratic function?
\newline
y
=
x
2
−
10
x
+
21
y = x^2 - 10x + 21
y
=
x
2
−
10
x
+
21
\newline
Choices:
\newline
(A)
y
∣
y
≥
5
{y | y \geq 5}
y
∣
y
≥
5
\newline
(B)
y
∣
y
≤
5
{y | y \leq 5}
y
∣
y
≤
5
\newline
(C)
y
∣
y
≥
−
4
{y | y \geq -4}
y
∣
y
≥
−
4
\newline
(D)all real numbers
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5
5
5
Find the values of the constant
c
c
c
for which the line
4
y
=
2
x
+
c
4 y=2 x+c
4
y
=
2
x
+
c
is a tangent to th curve
y
=
4
x
+
8
x
y=4 x+\frac{8}{x}
y
=
4
x
+
x
8
.
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Select all the expressions that are equivalent to
3
6
×
9
6
3^6 \times 9^6
3
6
×
9
6
.
\newline
Multi-select Choices:
\newline
(A)
1
2
7
−
6
\frac{1}{27^{-6}}
2
7
−
6
1
\newline
(B)
2
7
12
27^{12}
2
7
12
\newline
(C)
1
2
7
6
\frac{1}{27^6}
2
7
6
1
\newline
(D)
2
7
36
27^{36}
2
7
36
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Multiply complex numbers
\newline
−
12
⋅
(
8
−
2
i
)
=
□
-12 \cdot(8-2 i)=\square
−
12
⋅
(
8
−
2
i
)
=
□
\newline
Your answer should be a complex number in the form
a
+
b
i
a+b i
a
+
bi
where
a
a
a
and
b
b
b
are real numbers.
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Which of the following is a correct interpretation of the expression
\newline
−
6
+
9
-6+9
−
6
+
9
?
\newline
Choose
1
1
1
answer:
\newline
(A) The number that is
9
9
9
to the left of
−
6
-6
−
6
on the number line
\newline
(B) The number that is
9
9
9
to the right of
−
6
-6
−
6
on the number line
\newline
(C) The number that is
6
6
6
to the left of
−
9
-9
−
9
on the number line
\newline
(D) The number that is
6
6
6
to the right of
−
9
-9
−
9
on the number line
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Let
g
g
g
be a continuous function on the closed interval
[
−
1
,
3
]
[-1,3]
[
−
1
,
3
]
, where
g
(
−
1
)
=
−
2
g(-1)=-2
g
(
−
1
)
=
−
2
and
g
(
3
)
=
−
5
g(3)=-5
g
(
3
)
=
−
5
.
\newline
Which of the following is guaranteed by the Intermediate Value Theorem?
\newline
Choose
1
1
1
answer:
\newline
(A)
g
(
c
)
=
−
3
g(c)=-3
g
(
c
)
=
−
3
for at least one
c
c
c
between
−
1
-1
−
1
and
3
3
3
\newline
(B)
g
(
c
)
=
−
3
g(c)=-3
g
(
c
)
=
−
3
for at least one
c
c
c
between
−
5
-5
−
5
and
−
2
-2
−
2
\newline
(C)
g
(
c
)
=
0
g(c)=0
g
(
c
)
=
0
for at least one
c
c
c
between
−
5
-5
−
5
and
−
2
-2
−
2
\newline
(D)
g
(
c
)
=
0
g(c)=0
g
(
c
)
=
0
for at least one
c
c
c
between
−
1
-1
−
1
and
3
3
3
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What is the amplitude of
y
=
3
sin
(
2
x
−
1
)
+
4
y=3 \sin (2 x-1)+4
y
=
3
sin
(
2
x
−
1
)
+
4
?
\newline
units
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What is the amplitude of
y
=
−
3
cos
(
π
x
+
2
)
−
6
?
y=-3 \cos (\pi x+2)-6 ?
y
=
−
3
cos
(
π
x
+
2
)
−
6
?
\newline
units
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What is the amplitude of
y
=
5
sin
(
4
x
−
2
)
−
3
y=5 \sin (4 x-2)-3
y
=
5
sin
(
4
x
−
2
)
−
3
?
\newline
units
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What is the amplitude of
\newline
g
(
x
)
=
−
2
sin
(
π
2
x
−
3
)
+
5
?
g(x)=-2 \sin \left(\frac{\pi}{2} x-3\right)+5 ?
g
(
x
)
=
−
2
sin
(
2
π
x
−
3
)
+
5
?
\newline
units
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What is the amplitude of
h
(
x
)
=
−
4
sin
(
2
x
−
7
)
+
3
h(x)=-4 \sin (2 x-7)+3
h
(
x
)
=
−
4
sin
(
2
x
−
7
)
+
3
?
\newline
units
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The functions
f
(
x
)
=
8
(
2
5
)
x
f(x)=8\left(\frac{2}{5}\right)^{x}
f
(
x
)
=
8
(
5
2
)
x
and
g
(
x
)
=
8
(
b
)
x
g(x)=8(b)^{x}
g
(
x
)
=
8
(
b
)
x
are graphed in the
x
y
x y
x
y
-plane. For what value of
b
b
b
would the graphs of functions
f
f
f
and
g
g
g
be symmetric with respect to the
y
y
y
-axis?
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The equation
s
=
(
t
+
3
)
2
(
t
+
2
)
(
t
+
1
)
(
t
)
(
t
−
1
)
s=(t+3)^{2}(t+2)(t+1)(t)(t-1)
s
=
(
t
+
3
)
2
(
t
+
2
)
(
t
+
1
)
(
t
)
(
t
−
1
)
is graphed on the
s
t
s t
s
t
-plane. What is the product of the unique
t
t
t
-intercepts of the graph?
\newline
□
\square
□
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What is the range of this quadratic function?
\newline
y
=
x
2
+
8
x
+
16
y = x^2 + 8x + 16
y
=
x
2
+
8
x
+
16
\newline
Choices:
\newline
(A)
{
y
∣
y
≥
0
}
\left\{y\mid y \geq 0\right\}
{
y
∣
y
≥
0
}
\newline
(B)
{
y
∣
y
≤
0
}
\left\{y\mid y \leq 0\right\}
{
y
∣
y
≤
0
}
\newline
(C)
{
y
∣
y
≥
−
4
}
\left\{y\mid y \geq -4\right\}
{
y
∣
y
≥
−
4
}
\newline
(D) all real numbers
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